near the end of halo reach (which was by all means a great game, my favourite in fact), Jun and Dr Halsey departed in a pelican when Noble 6, Carter and Emile went to the MAC gun. But in Halo 4, Dr Halsey was still alive but in captivity by the UNSC, which must mean, yep you've guessed it, Jun must have survived. I'm not sure if this theory is correct after all, it is my theory, so if anyone form Bungie or anyone in fact could see if my theory could possibly be correct, because I just came up with this today, so it would be great for me to have an answer.
Thank you,
Jake Loughlen (GustaMeGaming on youtube)
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I have thought of this before and there is a huge possibility that he is still alive. When he attended Dr Halsey to CASTLE base in the highlands for Operation: WHITEGLOVE, we never saw him again. He either retired from service or continued his service to the UNSC and fought in the human-covenant war and either died in combat, he would have received a high reward for his actions on reach.